Maxima has a units package, as do the commercial software systems.
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sigoldberg1Dec 24 '10 at 19:17

1

Maybe throw Gnuplot into the mix? I love it for quick and easy plots of functions and data series, and when I then need something more polished I can very easily reuse the gnuplot code from other examples. Better than pointing and clicking to get results.
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LagerbaerApr 3 '11 at 16:11

1

SymPy should also probably be added to this list.
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SimonJun 25 '11 at 6:59

It is probably worth your while to buy Mathematica, Maple, or Matlab, depending on your needs. I wish it weren't so, but this is one area in which the commercial tools are still vastly better than their free counterparts.

If you are a student, you can buy these at fairly afforable prices. Maple 14 Student Edition is only $99. Mathematica for Students is \$140, and Matlab/Simulink is \$99 for students. It is also possible that your school or department already has a site license, allowing you to obtain and use this software for no additional cost.

For symbolic calculations, you want either Mathematica or Maple, with Maple being more user-friendly, and Mathematica being more prevalent (in my experience) in actual research environments. Matlab's focus is on numerical calculations.

Cadabra uses many of the same index algorithms as the Mathematica package xAct. Although xAct is more focused on General Relativity calculations, while Cadabra is more field theory oriented.
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SimonJun 25 '11 at 6:56

Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.
Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

Do you have any experience with it? If so, how does it compare in usefulness to Mathematica?
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nibotNov 4 '10 at 21:52

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I tend to use Python with Numpy barebones as it were, without the Sage environment around it. I prefer the combination of interactive and scripting methodologies which I can use with Python rather than the notebook methodology of Mathematica. Sage (at least through the web interface) is more like Mathematica and does cover many of the things you might do in Mathematica. I do sometimes crank up Mathematica to plot a quick graph (Manipulate is a great exploratory tool) but tend to get aggravated by things I would know how to do easily in Python.
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ihustonNov 4 '10 at 23:45

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If you are into Python, the combination of NumPy, SciPy and matplotlib will cover any need for numerical or scientific computing or graphing you may have. There also is a SymPy for symbolic calculations, but I have never used it. A friend of mine has his own open-source Python library for unit management: juanreyero.com/open/magnitude
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JaimeDec 27 '10 at 23:34

Thanks - I'll have a look at it. I spent some time playing with GiNaC about 1 year ago, but never really used it, since I couldn't justify learning it for my one off calculation. Instead, I took the computationally slow but familiar route of using Mathematica.
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SimonJun 25 '11 at 13:04

I used this software in my energy transfer courses, I never used it for symbolic, so I don't know if you can do symbolic computation, however it is very good at solving equations. As well as for conversions. It is not free, however you can download a student version, which I used the whole semester without problems. It is called ees. The company I think is called f chart. I know it is not exactly what you asked for, however it's a useful software to have around, especially when working with a lot of equations, since the software actually warns you about any inconsistency in the units.

It is also useful if you want to calculate say for example entropy, the software can do it for you if you have the pressure or temperature.